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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.1.g.a 152.g 152.g $1$ $0.076$ \(\Q\) \(\Q(\sqrt{-38}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b 152.g 152.g $1$ $0.076$ \(\Q\) \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
152.1.k.a 152.k 152.k $2$ $0.076$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
152.1.u.a 152.u 152.u $6$ $0.076$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
152.2.a.a 152.a 1.a $1$ $1.214$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b 152.a 1.a $1$ $1.214$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c 152.a 1.a $3$ $1.214$ 3.3.961.1 None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
152.2.b.a 152.b 152.b $2$ $1.214$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots\)
152.2.b.b 152.b 152.b $4$ $1.214$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
152.2.b.c 152.b 152.b $12$ $1.214$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
152.2.c.a 152.c 8.b $2$ $1.214$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots\)
152.2.c.b 152.c 8.b $16$ $1.214$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
152.2.i.a 152.i 19.c $2$ $1.214$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b 152.i 19.c $2$ $1.214$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c 152.i 19.c $6$ $1.214$ 6.0.2696112.1 None None \(0\) \(-1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.2.o.a 152.o 152.o $4$ $1.214$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.b 152.o 152.o $4$ $1.214$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.c 152.o 152.o $28$ $1.214$ None None \(-3\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
152.2.p.a 152.p 152.p $36$ $1.214$ None None \(-1\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$
152.2.q.a 152.q 19.e $6$ $1.214$ \(\Q(\zeta_{18})\) None None \(0\) \(-6\) \(6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b 152.q 19.e $6$ $1.214$ \(\Q(\zeta_{18})\) None None \(0\) \(9\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c 152.q 19.e $18$ $1.214$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
152.2.t.a 152.t 152.t $108$ $1.214$ None None \(-6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
152.2.v.a 152.v 152.v $12$ $1.214$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
152.2.v.b 152.v 152.v $96$ $1.214$ None None \(-6\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
152.3.e.a 152.e 19.b $2$ $4.142$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(14\) \(22\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots\)
152.3.e.b 152.e 19.b $8$ $4.142$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-14\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
152.3.f.a 152.f 8.d $36$ $4.142$ None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
152.3.g.a 152.g 152.g $3$ $4.142$ 3.3.4104.1 \(\Q(\sqrt{-38}) \) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.b 152.g 152.g $3$ $4.142$ 3.3.4104.1 \(\Q(\sqrt{-38}) \) None \(6\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.c 152.g 152.g $32$ $4.142$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
152.3.k.a 152.k 152.k $4$ $4.142$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(4\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots\)
152.3.k.b 152.k 152.k $72$ $4.142$ None None \(-5\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
152.3.l.a 152.l 152.l $76$ $4.142$ None None \(-3\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$
152.3.n.a 152.n 19.d $20$ $4.142$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
152.3.r.a 152.r 19.f $60$ $4.142$ None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
152.3.s.a 152.s 152.s $228$ $4.142$ None None \(-6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
152.3.u.a 152.u 152.u $12$ $4.142$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
152.3.u.b 152.u 152.u $216$ $4.142$ None None \(-6\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
152.4.a.a 152.a 1.a $2$ $8.968$ \(\Q(\sqrt{57}) \) None None \(0\) \(-1\) \(-5\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots\)
152.4.a.b 152.a 1.a $3$ $8.968$ 3.3.3221.1 None None \(0\) \(-5\) \(2\) \(-35\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
152.4.a.c 152.a 1.a $3$ $8.968$ 3.3.7057.1 None None \(0\) \(4\) \(7\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
152.4.a.d 152.a 1.a $5$ $8.968$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(2\) \(0\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
152.4.b.a 152.b 152.b $2$ $8.968$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots\)
152.4.b.b 152.b 152.b $56$ $8.968$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
152.4.c.a 152.c 8.b $54$ $8.968$ None None \(2\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$
152.4.i.a 152.i 19.c $14$ $8.968$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(5\) \(5\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
152.4.i.b 152.i 19.c $16$ $8.968$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-5\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.4.o.a 152.o 152.o $4$ $8.968$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-30\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b 152.o 152.o $112$ $8.968$ None None \(-3\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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